Neuromorphic hardware combines memory (synapses) and computation (neurons) into the same silicon substrate to avoid the von-Neumann bottleneck. This way, neuromorphic computing aims to make computational neuroscience simulations and AI processing faster and more energy-efficient. The common crossbar architecture integrates a synapse matrix (analog, mixed-signal or digital) with a neuron array into a neurosynaptic core, whereas multiple cores are interconnected via a dedicated spike routing network. One of such neuromorphic architecture is the BrainScaleS wafer-scale system which allows the realization of very flexible network architecture, supporting both dense and sparse connectivity by highly configurable neurosynaptic cores. Yet, when network models from computational neuroscience are mapped to the BrainScaleS wafer, synapse loss can occur which means that for some model synapses no hardware synapse is available due to the restricted connectivity of the hardware. In this work we analyze the synapse loss when mapping uniform random networks to BrainScaleS both theoretically and empirically. We first develop a methodology to estimate maximum-sized networks without synapse loss based on probability distributions and the hardware's synapse routing architecture. Next, we adopt the methodology to predict the synapse loss for denser or larger network models. Then, we compare the predictions with results from actual runs of the mapping software: The results show the capabilities and limitations of the BrainScaleS system itself and spot shortcomings of the current mapping algorithms. The developed methodology can be helpful in multiple ways: to find the optimal settings when mapping a given network model to BrainScaleS, to act as a benchmark for the mapping software, and as tool for design space exploration for new hardware.

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